QCD Corrections to Hadronic Higgs Decays

DESY 95–210 KA–TP–8–95 hep-ph/9511344 November 1995

arXiv:hep-ph/9511344v1 16 Nov 1995

QCD Corrections to Hadronic Higgs Decays

A. Djouadi1,2∗ , M. Spira3 and P.M. Zerwas2

1

2

Institut f¨ ur Theoretische Physik, Universit¨at Karlsruhe, D–76128 Karlsruhe, FRG.

Deutsches Elektronen–Synchrotron DESY, D-22603 Hamburg, FRG. 3

II. Institut f¨ ur Theoretische Physik† , D-22761 Hamburg, FRG.

Abstract

We present an update of the branching ratios for Higgs decays in the Standard Model and the Minimal Supersymmetric extension of the Standard Model. In particular, the decays of the Higgs particles to quark and gluon jets are analyzed and the spread in the theoretical predictions due to uncertainties of the quark masses and the QCD coupling is discussed.

∗

Supported by Deutsche Forschungsgemeinschaft DFG (Bonn). Supported by Bundesministerium f¨ ur Bildung und Forschung (BMBF), Bonn, under Contract 05 6 HH 93P (5), and by EU Program Human Capital and Mobility through Network Physics at High Energy Colliders under Contract CHRX–CT93–0357 (DG12 COMA). †

1. Introduction The coupling of the Higgs bosons to other particles grows with the mass of the particles. This characteristic property is a direct consequence of mass generation through the Higgs mechanism. To establish the Higgs mechanism experimentally, it is therefore mandatory to measure the couplings very accurately [1] once scalar particles have been found. The main test grounds for the Higgs couplings to gauge bosons are the production cross sections for Higgs-strahlung off gauge bosons and W W/ZZ fusion, and the widths/branching ratios for Higgs decays to gauge bosons. The Higgs couplings to heavy quarks determine the cross sections for the production of Higgs particles in gg fusion at hadron colliders [2, 3], as well as the rate of Higgs bremsstrahlung off heavy quarks at e+ e− [4] and hadron colliders [5]. The measurement of Higgs decay branching ratios, including b, c quarks and τ leptons [6], provides a complementary method to determine the Higgs couplings. In this note we will reanalyze [7] the branching ratios for Higgs decays to b, c quark jets and to light hadron jets evolving out of gluon decays, H → bb / cc + . . . H → gg + . . .

(1) (2)

The ellipses indicate additional gluon and quark partons in the final state due to QCD radiative corrections. Special attention will be paid to uncertainties related to the b, c quark masses and the QCD coupling αs . It turns out that the evolution of the charm quark mass from low energy scales, where it can be determined by QCD sum rules, to high energy scales defined by the Higgs mass, introduces very large uncertainties in the cc branching ratio. The partial width of the second decay mode (2) will be derived for gluon and light quark final states since heavy quarks add to the partial width of the first decay process (1). The b, c and gluon decay modes are experimentally important in the Standard Model (SM) for Higgs masses less than about 150 GeV. In the minimal supersymmetric extension (MSSM) b quark decays may be dominant for a much wider range in the parameter space.

2. Standard Model 2.1 b, c quark decays of the SM Higgs particle The particle width for decays to (massless) b, c quarks directly coupled to the SM Higgs particle is given, up to O(αs2 ) QCD radiative corrections1 , (Fig.1a) by the well-known expression [8, 9, 10] Γ[H → QQ] = 1

3GF MH 2 √ mQ (MH ) [∆QCD + ∆t ] 4 2π

The effect of the electroweak radiative corrections in the branching ratios is negligible [11].

2

(3)

∆QCD

αs (MH ) αs (MH ) + (35.94 − 1.36NF ) = 1 + 5.67 π π

∆t =

αs (MH ) π

!2 "

!2

m2Q (MH ) 1 2 M2 1.57 − log H2 + log2 3 Mt 9 MH2

#

in the MS renormalization scheme; the running quark mass and the QCD coupling are defined at the scale of the Higgs mass, absorbing this way any large logarithms. The quark masses can be neglected in general except for top quark decays where this approximation holds only sufficiently far above threshold; the QCD correction in this case are given in the Appendix. Since the relation between the pole mass Mc of the charm quark and the MS mass evaluated at the pole mass mc (Mc ) is badly convergent [12], we will adopt the running quark masses mQ (MQ ) as starting points. They have been extracted directly from QCD sum rules evaluated in a consistent O(αs ) expansion [13]. The evolution from MQ upwards to a renormalization scale µ is given by mQ (µ) = mQ (MQ )

c [αs (µ)/π] c [αs (MQ )/π]

(4)

with [9, 12] 25 12 x) 25 [1 + 1.014x + 1.389 x2] 6 23 12 c(x) = ( x) 23 [1 + 1.175x + 1.501 x2] 6 c(x) = (

for Mc < µ < Mb for Mb < µ

For the charm quark mass the evolution is determined by eq.(4) up to the scale µ = Mb , while for scales above the bottom mass the evolution must be restarted at MQ = Mb . Typical values of the running b, c masses at the scale µ = 100 GeV, characteristic for the Higgs mass, are displayed in Table 1. The evolution has been calculated for the QCD coupling αs (MZ ) = 0.118 ± 0.006

(5)

defined at the Z mass [14]. The large uncertainty in the running charm mass is a consequence of the small scale at which the evolution starts and where the errors of the QCD coupling are very large. 2.2 Higgs decay to light hadron jets The decay of the Higgs boson to gluons is mediated by heavy quark loops in the Standard Model (Fig.1b); the partial decay width [15] is given by ΓLO [H → gg] =

GF αs2

M3 √ H 36 2 π 3 3

2 X H A (τQ ) t,b

(6)

αs (MZ )

mQ (MQ )

MQ = MQpt2

mQ (µ = 100 GeV)

b

0.112 0.118 0.124

(4.26 ± 0.02) GeV (4.23 ± 0.02) GeV (4.19 ± 0.02) GeV

(4.62 ± 0.02) GeV (4.62 ± 0.02) GeV (4.62 ± 0.02) GeV

(3.04 ± 0.02) GeV (2.92 ± 0.02) GeV (2.80 ± 0.02) GeV

c

0.112 0.118 0.124

(1.25 ± 0.03) GeV (1.23 ± 0.03) GeV (1.19 ± 0.03) GeV

(1.42 ± 0.03) GeV (1.42 ± 0.03) GeV (1.42 ± 0.03) GeV

(0.69 ± 0.02) GeV (0.62 ± 0.02) GeV (0.53 ± 0.02) GeV

Table 1: The running b, c quark masses in the MS renormalization scheme at the scale µ = 100 GeV. The starting points mQ (MQ ) of the evolution are extracted from QCD sum rules [13]; the pole masses MQpt2 are defined by the O(αs ) relation mQ (MQpt2 ) = MQpt2 /[1 + 4αs /3π] with the running masses. with the form factor AH (τ ) =

3

τ [1 + (1 − τ )f (τ )] 1 arcsin2 √ τ ≥1 τ √ " # 2 f (τ ) =  1+ 1−τ 1   √ τ 200 GeV], (c) and (d). In figure (a) the curves for the upper and lower limit of the top mass band are presented separately, using the average values of the other quark masses and of the strong coupling αs for the sake of clarity. The labels follow the definitions in Fig.2; i.e. the branching ratios are classified according to the inclusive hadronic final states with [labels b¯b, c¯ c] and without heavy quarks [label gg].

12

(a)

q

q

g H

H

_

_

q

q

(b)

g

q

g

q

g Q

_

Q

H

Q H

H g

g

g

Fig. 1

1 _

bb Standard Model BR(HSM)

10

-1

ττ

+ _

cc

gg 10

-2

*

*

WW

* *

ZZ 60

70

80

90

100

110

MH [GeV] Fig. 2

13

120

130

140

150

1

_

bb MSSM: BR(h) tgβ = 1.6 A = -µ = 1 TeV

10

165

176

187

ττ

+ -

-1

Mt = 165

176

187

_

cc

10

gg

-2

W*W* 50

60

70

80

90

100

110

Mh [GeV] Fig. 3a

1

BR(H) tgβ = 1.6 A = -µ = 1 TeV tt 10

*

-1

_

bb

10

-2

ττ

+ -

_

cc 100

200

MH [GeV] Fig. 3b

14

300

400

1

BR(H) tgβ = 1.6 A = -µ = 1 TeV *

*

WW 10

10

-1

* *

ZZ

-2

gg

100

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400

MH [GeV]

1

hh

10

BR(H) tgβ = 1.6 A = -µ = 1 TeV

-1

*

ZA

10

-2

*

±

WH

AA 100

200

MH [GeV] Fig. 3b cont'd

15

300

400

1

_

bb

tt

BR(A) tgβ = 1.6 A = -µ = 1 TeV

10

*

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Zh ττ

+ -

-1

gg

10

-2

_

cc 50

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70 80 90 100

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MA [GeV] Fig. 3c

1

τν

±

BR(H ) tgβ = 1.6 A = -µ = 1 TeV

10

-1

*

*

WA

Wh

*

tb

cs cb 10

-2

80

100

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140

MH± [GeV] Fig. 3d

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